To find the value of n, we need to determine the pattern of the sequence and then find the general formula for the nth term.
From 3 to 9, we add 6.
From 9 to 15, we add 6.
From 15 to 21, we add 6.
Therefore, the sequence has a common difference of 6.
The formula for the nth term of an arithmetic sequence is given by: tn = a + (n - 1)d, where a is the first term and d is the common difference.
In this case, the formula is: tn = 3 + (n - 1)6.
Now, we need to find the value of n when the sum of the sequence is 7500.
The sum of an arithmetic series is given by the formula: Sn = (n/2)(a + tn), where Sn is the sum of the first n terms.
In this case, Sn = 7500 and a = 3. Substituting the values into the formula:
7500 = (n/2)(3 + (3 + (n - 1)6))
7500 = (n/2)(3 + 3 + 6n - 6)
7500 = (n/2)(6n)
7500 = 3n^2
2500 = n^2
n = √2500
n = 50 or n = -50
Since n represents the number of terms in the sequence, it cannot be negative. Therefore, the value of n is 50.
The sum of n terms of the sequence 3,9,15,21 is 7500 determine value if n
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